It depends on how you want to edit it.

If you want to edit the name itself (changing it from "Shergar" to "Red Rum" for example), you still use the Edit Profile route as normal.

If you want to edit the colours etc, hover your mouse over the horse and click on the Lyre icon that appears just underneath it.

Just to add, each time you edit the name via Edit Profile it'll reset the Lyre effects so you'll have to redo that step.

Thank you - realised what I was doing wrong! Locking now as solved.